• Journal of applied mathematics & informatics
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• 제40권3_4호
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• pp.675-694
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• 2022

In this article, we investigate the solution of the inverse problem for one dimensional heat equation with Neumann and Robin boundary conditions, that is, we determine the temperature and source term with given initial and boundary conditions. Three radial basis functions(RBFs) have been used for numerical solution, and Homotopy perturbation method for analytic solution. Numerical solutions which are obtained by considering each of the three RBFs are compared to the exact solution. For appropriate value of shape parameter c, numerical solutions best approximates exact solutions. Furthermore, we have shown the impact of noisy data on the numerical solution of u and f.

• Structural Engineering and Mechanics
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• 제74권5호
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• pp.679-698
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• 2020

In this paper, the meshless local Petrov-Galerkin (MLPG) method is developed for dynamic analysis of non-symmetric nanocomposite cylindrical shell equations of elastic wave motion with nonlinear grading patterns under shock loading. The mechanical properties of the nanocomposite cylinder are obtained based on a micro-mechanical model. In this study, four kinds of grading patterns are assumed for carbon nanotube mechanical properties. The displacements can be approximated using shape function so, the multiquadrics (MQ) Radial Basis Functions (RBF) are used as the shape function. In order to discretize the derived equations in time domains, the Newmark time approximation scheme with suitable time step is used. To demonstrate the accuracy of the present method for dynamic analysis, at the first a problem verifies with analytical solution and then the present method compares with the finite element method (FEM), finally, the present method verifies by using the element free Galerkin (EFG) method. The comparison shows the high capacity and accuracy of the present method in the dynamic analysis of cylindrical shells. The capability of the present method to dynamic analysis of non-symmetric nanocomposite cylindrical shell is demonstrated by dynamic analysis of the cylinder with different kinds of grading patterns and angle of nanocomposite reinforcements. The present method shows high accuracy, efficiency and capability to dynamic analysis of non-symmetric nanocomposite cylindrical shell, which it furnishes a ground for a more flexible design.

• International Journal of Fluid Machinery and Systems
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• 제10권3호
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• pp.240-253
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• 2017

Latin hypercube sampling is widely used design-of-experiment technique to select design points for simulation which are then used to construct a surrogate model. The exploration/exploitation properties of surrogate models depend on the size and distribution of design points in the chosen design space. The present study aimed at evaluating the performance characteristics of various surrogate models depending on the Latin hypercube sampling (LHS) procedure (sample size and spatial distribution) for a diverse set of optimization problems. The analysis was carried out for two types of problems: (1) thermal-fluid design problems (optimizations of convergent-divergent micromixer coupled with pulsatile flow and boot-shaped ribs), and (2) analytical test functions (six-hump camel back, Branin-Hoo, Hartman 3, and Hartman 6 functions). The three surrogate models, namely, response surface approximation, Kriging, and radial basis neural networks were tested. The important findings are illustrated using Box-plots. The surrogate models were analyzed in terms of global exploration (accuracy over the domain space) and local exploitation (ease of finding the global optimum point). Radial basis neural networks showed the best overall performance in global exploration characteristics as well as tendency to find the approximate optimal solution for the majority of tested problems. To build a surrogate model, it is recommended to use an initial sample size equal to 15 times the number of design variables. The study will provide useful guidelines on the effect of initial sample size and distribution on surrogate construction and subsequent optimization using LHS sampling plan.

• 한국기계가공학회지
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• 제20권6호
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• pp.33-43
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• 2021

A60 class bulkhead penetration piece is a fire resistance system installed on a bulkhead compartment to protect lives and to prevent flame diffusion in a fire accident on a ship and offshore plant. This study focuses on the approximate optimization of the fire resistance design of the A60 class bulkhead penetration piece using a multi-island genetic algorithm. Transient heat transfer analysis was performed to evaluate the fire resistance design of the A60 class bulkhead penetration piece. For approximate optimization, the bulkhead penetration piece length, diameter, material type, and insulation density were considered discrete design variables; moreover, temperature, cost, and productivity were considered constraint functions. The approximate optimum design problem based on the meta-model was formulated by determining the discrete design variables by minimizing the weight of the A60 class bulkhead penetration piece subject to the constraint functions. The meta-models used for the approximate optimization were the Kriging model, response surface method, and radial basis function-based neural network. The results from the approximate optimization were compared to the actual results of the analysis to determine approximate accuracy. We conclude that the radial basis function-based neural network among the meta-models used in the approximate optimization generates the most accurate optimum design results for the fire resistance design of the A60 class bulkhead penetration piece.

• Structural Engineering and Mechanics
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• 제88권3호
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• pp.239-249
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• 2023

The Radial Point Interpolation Method (RPIM) has been proposed to overcome the difficulties associated with the use of the Radial Basis Functions (RBFs). The RPIM has the following properties: Simple implementation in terms of boundary conditions as in the Finite Element Method (FEM). A less expensive CPU time compared to other collocation meshless methods such as the Moving Least Square (MLS) collocation method. In this work, we propose an adaptive high-order numerical algorithm based on RPIM to simulate the thermoviscoplastic behavior of a material mixing observed in the Friction Stir Welding (FSW) process. The proposed adaptive meshfree RPIM algorithm adapts well to the geometric and physical data by choosing a good shape parameter with a good precision. Our numerical approach combines the RPIM and the Asymptotic Numerical Method (ANM). A numerical procedure is also proposed in this work to automatically determine an improved shape parameter for the RBFs. The efficiency of the proposed algorithm is analyzed in comparison with an iterative algorithm.

• 한국음향학회지
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• 제18권8호
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• pp.94-99
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• 1999

성 인식 알고리즘에서 높은 인식률을 보이는 방법은 hidden Markov mode1(HMM)과 신경망의 혼합 형태이다. 이것은 통계적인 모델과 신경망 모델의 장점을 혼용하는 방법이다. 본 연구에서 제안하는 인식 알고리듬은 반연속 HMM과 radial basis function(RBF)의 새로운 형태의 혼합 구조로써 반연속 HMM 파라미터 중에서 관측 확률을 결정하는 가중치(혼합확률밀도함수계수)확률을 Baum-Welch 추정 이후 RBF로로써 재 추정하는 인식 모델을 제안한다. 제안한 방법은 RBF의 은닉층(hidden layer)의 기본 함수(basis function)와 반연속 HMM의 확률 밀도 함수의 유사함을 고려한 것으로 RBF의 학습 및 추정된 가중치로써 보다 음성 파형을 분별력 있게 구분하고자 하는 것이다. 모의 실험 결과는 반연속 HM만을 사용 할 때 보다 제안한 반연속 HMM/RBF 혼합 구조가 비 학습 화자에 대한 인식률을 개선함으로써 단순히 반연속 HMM만을 사용하는 것 보다 훨씬 분별력이 높은 방법임을 보여준다.

• 전자공학회논문지CI
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• 제43권6호
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• pp.34-42
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• 2006

데이터 마이닝(data mining)이란 대량의 데이터에 내재되어 있는 숨겨진 패턴을 찾아내기 위한 분석 기술로서 지금까지 많은 연구가 진행되어 왔지만, 현재의 데이터 마이닝 연구는 ad-hoc 문제와 같은 해결되어야 할 중요한 이슈들이 있다. 즉, 개별적 문제에 대해 설계된 마이닝 기법이 주로 사용되는 까닭에 여러 문제에 통합적으로 적용될 수 있는 시스템적 마이닝 기법에 관한 연구가 요구되고 있다. 본 논문에서는 이러한 핵심 데이터 마이닝 태스크 중의 하나인 분류 모델링 방법으로 방사형 기저 함수(radial basis function, RBF) 모델의 성능을 고찰하고 그 유용성(usefulness)을 살펴보고자 한다. 특히, 대표적인 마이닝 관련 벤치마킹 데이터인 Monk's problem 분석을 위해 RC(Representation Capacity) 기반 알고리즘을 사용하여 RBF 모델을 구축하고 분류 성능을 기존의 연구 결과와 비교 고찰한다. 그리하여 RBF 모델의 분류 성능 면에서의 우수성뿐만 아니라 모델링 과정을 체계적인 방식으로 적절히 제어할 수 있음을 보여주고, 이를 통해 현재의 ad-hoc 방식의 문제를 어느 정도 해결할 수 있음을 보여준다.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2003년도 ISIS 2003
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• pp.78-81
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• 2003

This paper proposes a fuzzy classifier system (FCS) using hyper-cone membership functions (HCMFs) and rule reduction techniques. The FCS can generate excellent rules which have the best number of rules and the best location and shape of membership functions. The HCMF is expressed by a kind of radial basis function, and its fuzzy rule can be flexibly located in input and output spaces. The rule reduction technique adopts a decreasing method by merging the two appropriate rules. We applay the FCS to a tubby rule generation for the inverted pendulum control.

• 한국지능시스템학회논문지
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• 제6권3호
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• pp.25-36
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• 1996

기존의 RBF 신경망 및 퍼지 시스템을 고차원 입력 공간 위에서의 비선형 근사에 적용할 경우 은닉 노드의 수혹은 퍼지 IF-THEN 규칙의 수가 기하급수적으로 증가한다. 본 논문에서는 이러한 문제점을 개선하기 위해 반국소 유닛을 기본 요소로 하는 수목구조지능시스템을 제안하고, 이를 효과적으로 학습하기 위하여 수정 유전자 알고리즘 및 LMS 규칙에 기반을 둔 학습 알고리즘을 개발한다. 제안된 시스템에 대한 근사 능력 해석이 수행되고, 실험적 고찰을 통하여 개발된 방법론의 유용성이 입증된다.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제11권8호
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• pp.4043-4060
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• 2017

Network Intrusion Detection (NID), an important topic in the field of information security, can be viewed as a pattern recognition problem. The existing pattern recognition methods can achieve a good performance when the number of training samples is large enough. However, modern network attacks are diverse and constantly updated, and the training samples have much smaller size. Furthermore, to improve the learning ability of SVM, the research of kernel functions mainly focus on the selection, construction and improvement of kernel functions. Nonetheless, in practice, there are no theories to solve the problem of the construction of kernel functions perfectly. In this paper, we effectively integrate the advantages of the radial basis function kernel and the polynomial kernel on the notion of the game theory and propose a novel kernel SVM algorithm with game theory for NID, called GTNID-SVM. The basic idea is to exploit the game theory in NID to get a SVM classifier with better learning ability and generalization performance. To the best of our knowledge, GTNID-SVM is the first algorithm that studies ensemble kernel function with game theory in NID. We conduct empirical studies on the DARPA dataset, and the results demonstrate that the proposed approach is feasible and more effective.